Quantum mechanics Definition and 994 Threads

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
Classical physics, the description of physics that existed before the theory of relativity and quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, while quantum mechanics explains the aspects of nature at small (atomic and subatomic) scales, for which classical mechanics is insufficient. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).
Quantum mechanics arose gradually from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. These early attempts to understand microscopic phenomena, now known as the "old quantum theory", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield.

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  1. S

    A Does Feynman's path integral ignore alternative histories?

    Summary: Does Richard Feynman's multiple histories ignore alternative histories? Did Richard Feynman's multiple histories (https://en.wikipedia.org/wiki/Multiple_histories) ignore the existence of other alternarive histories or paths? I ask this referring to this comment from this page...
  2. B

    Where is a particle most likely to be? (Griffiths Quantum Mechanics)

    The wave function described seems impossible. Wave functions have to be differentiable at all points, right? Otherwise they don't represent a physically realizable state. The wave function in the example isn't differentiable at x=A, the maximum point. Also, for problem (c), I know it's visually...
  3. P

    A Can decoherence be associated with heat generation?

    This question is inspired by a comment that @thephystudent made where he said that "The dephasing between the Bragg pulses is not unitary, I believe it can be explicitly written in Lindblad form and generates heat. I believe this Point of view is the same as (among others) the papers of...
  4. S

    A Does Bohmian Mechanics yield the existence of a multiverse?

    David Deutsch, a theoretical physicist, talks about David Bohm in his book "the Fabric of Reality": "[w]orking out what Bohm’s invisible wave will do requires the same computations as working out what trillions of shadow photons will do. Some parts of the wave describe us, the observers...
  5. H

    A Quantum Mechanics: Exploring Symmetry and Continuation

    Does quantum mechanics follow causality, phase transition, critical point, symmetry, asymmetry, order, disorder, continuation, discontinuation, limitation, without limitation, convergence, divergence, similarity, hierarchical structure, singularity, plurality?
  6. jdou86

    How do I understand spin in quantum mechanics for Physics GRE question 2?

    Summary: please help me understand the following questions from Physics GRE test Thank you very much! To be honest i really hate this formalism. Memorizing such things is pain. but like everything it is what it is
  7. S

    Could MWI create universes with fundamentally different physical laws?

    Summary: Could MWI (Many Worlds Interpretation) create universes with fundamentally different physical laws? Physicist John Wheeler proposed along with Hugh Everett and Bryce DeWitt the 'Many Worlds' Interpretation of Quantum Mechanics (although he expressed some doubts about its validity) I...
  8. M

    I Double Slit Experiment question

    I read in a book the following assertion. In a double slit experiment photons are passed through the slits and detected at the end plate. Each of the two slits has a quarter wave plate which alters the polarization of the photons that pass through it in a way different than the other QWP. Thus a...
  9. M

    I Why does quantum mechanics believe that gravity is a field?

    According to general relativity, gravity is simply the side-effect of bending the geometry of space-time. As a thought experiment imagine a 3D image being projected from a 2D hologram - the distance between the actual 2D pixels in the 2D plane always remains constant, yet depending on the shape...
  10. D

    QFT for Gifted Amateur - Problem 2.2

    I'm getting confused by the perturbation theory aspect of problem 2.2 in this book. We have to show that the energy eigenvalues are given by $$E_n = \left(n + \frac{1}{2}\right) \hbar \omega + \frac{3\lambda}{4} \left(\frac{\hbar}{m\omega}\right)^2 (2n^2 + 2n + 1)$$ For the Hamiltonian...
  11. Haorong Wu

    I Are time and space continuous or discrete?

    In another forum, some people argue that time and space are discrete, due to Planck time and Planck length. However, I disagree with this idea. I think, the Planck time and Planck length are just some scales that we can measure, but they do not forbid continuous time and space shorter than...
  12. D

    Courses Graduate Quantum as an Undergrad

    Hello, I'm considering taking the graduate level quantum mechanics course offered at my university (based on Sakurai/Shankar). I am currently reading Sakurai's QM, and mostly understand the topics (I'm currently reading the theory of angular momentum). There have been some steps where I still...
  13. T

    I What makes the interpretations of Quantum Mechanics so important?

    How valid is the statement "It means physics is ultimately concerned with descriptions of the real world" in the realm of QM? Heretic question, what is "real" besides the outcome of the measurement?
  14. adosar

    I Momentum operator in quantum mechanics

    The momentum operator for one spation dimension is -iħd/dx (which isn't a vector operator) but for 3 spatial dimensions is -iħ∇ which is a vector operator. So is it a vector or a scalar operator ?
  15. M

    A Is time irrelevant in quantum mechanics?

    Could one come to think that time is irrelevant in quantum mechanics? we know that the QM equations are written with the time variable, (schrodinger equation). Yet everything suggests that time is irrelevant, as the search for loop quantum gravity seems to indicate
  16. D

    Quantum Should I Get Both of Dirac's Quantum Mechanics Books?

    Hello, I remembered once hearing of a must-have quantum mechanics book by Paul Dirac. I don't remember if it was his Principles of QM or Lectures on QM. Based on the table of contents, I believe it was the Principles of QM book; however, looking at both I was thinking about getting his Lectures...
  17. W

    I Relativistic Quantum Mechanics & Localized Particles

    A lecturer today told the class that relativistic QM for single particles is flawed by showing us that for a state centered at the origin, it was possible that ##Pr(\vec{x}>ct)>0##. He said that this was down to the fact that we should be considering multi-particle states in relativistic...
  18. L

    I The Cellular Automaton Interpretation of Quantum Mechanics

    Why aren't you guys discussing this? http://de.arxiv.org/abs/1405.1548 The paper is 259 pages. And it will take me a year to read it. The Cellular Automaton Interpretation of Quantum Mechanics doesn't use any wave function. Just please tell me. How does it explain for example the double slit...
  19. patric44

    Quantum What is the most suitable Quantum Mechanics book for these questions?

    i want to know what is the most suitable quantum mechanics that will enables me after studying it to answer these specific questions ? i mean based on the hardness of these questions ( what book would you suggest to study these subjects ) . and by the way what is the level of these QM questions...
  20. S

    I Is the Wheeler-DeWitt equation somehow related to the Multiverse?

    I've seen some articles that relate them (like this one: https://arxiv.org/pdf/1407.3118.pdf) "In this paper we will analyze the third quantization of gravity in path integral formalism. We will use the time-dependent version of WheelerDeWitt equation to analyze the multiverse in this...
  21. eliUCV

    I Quantum Mechanics, The Delta-Function potential

    Hi, I have a question, why when we study the Delta-Function Potencial we can treat with ##E < V##, since the following relation says ##\frac{d^2 \psi}{dx^2} = \frac{2m}{\hbar^2} (V - E) \psi## And do not allow it? or it is just ##E <...
  22. R

    I Question About The Role of Observation in Quantum Mechanics

    In the double-slit experiment when a detector was placed before the two slits, a 2 strip pattern was produced after the two slits. When there was no detector placed before the two slits, a different pattern was produced after the two slits. Why does the presence of a detector before the two...
  23. R

    I Why Would Observation Change Anything Physically?

    A particle has a 33% chance of being in either position 1, position 2, or position 3. After I observe it, it is in position 1, and not in position 2 or 3. Questions: How do we know it was not already in that position prior to us observing it? Does observation cause position, or is position...
  24. R

    I Communicating Via Quantum Entanglement Using Time Differentiated Pulse

    Which of these premises is impossible or incorrect according to our current understanding of quantum entanglement? Given 2 entangled particles, p1 and p2: Observing paired particle p1 induces a change in spin on paired particle p2. There a way of detecting a change in spin on particle p2...
  25. A. Neumaier

    I Exploring Quantum Gravity's Impact on Quantum Mechanics

    See Peter Shor's comments here and here and Urs Schreiber's comments here.
  26. J

    A Does the effective action make sense in Quantum Mechanics?

    I think the effective action should make sense also in Quantum Mechanics, not only in QFT. But I have never seen described in a QM book as such. Could there be a QM book that uses effective actions? Or maybe in QM effective actions are called another name? I think effective actions in QM could...
  27. A. Neumaier

    I The Philosophy of Quantum Mechanics

    I'd like to point to the book The Philosophy of Quantum Mechanics by C. Friebe et al., Springer 2018. It contains many topics usually underrepresented in foundational discussions of quantum physics, in chapters on many-particle systems and quantum field theory. It also has in its last chapter a...
  28. F

    I Solving the Quantum Mechanics of a Hydrogen Atom

    Hello, I have a little problem understanding the quantum mechanics of a hydrogen atom. Im troubled with the following question: before i measure the state of a (simplified: without fine-, hyperfinestructure) hydrogen atom, which is the right probability density of finding the electron? is it...
  29. A. Neumaier

    A Jürg Fröhlich on the deeper meaning of Quantum Mechanics

    I'd like to draw attention to a very recent paper by Jürg Fröhlich, a well-known mathematical physicist from the ETH Zürich. It starts out as follows: Section 2 is titled ''Standard formulation of Quantum Mechanics and its shortcomings''. Surely @vanhees71 has very convincing reasons why this...
  30. Hawkingo

    I What is the failure of superposition in quantum mechanics?

    In a book it says that "we know of quantum phenomena in the electromagnetic field that represents a failure of superposition,seen from the viewpoint of the classical theory." I want to about what quantum phenomena is he talking about? This was from the page 11 of the book Electricity And...
  31. J

    A What does "solving a quantum mechanics problem" mean?

    In analogy to classical mechanics, I thought a good definition to "What does "solving a quantum mechanics problem" mean?" was to give the propagator (aka the Green function, or the 2-point correlation function): In classical mechanics, solving a problem means to give the path of the particle...
  32. A. Neumaier

    Insights The 7 Basic Rules of Quantum Mechanics

    Continue reading...
  33. Benhur

    How Do I Create the State Vector χ for Larmor Precession in a 2D B-field?

    I just tried to find the eigenvalues (for the energy), obtaining E = ±(γħ.√(Bo² + Γo²))/2 and the corresponding eigenvectors for the H matrix. But I don't know what to do to create de state vector χ.
  34. W

    How Do You Express the Tensor Product of Hamiltonians?

    ##U_1 \otimes U_2 = (1- i H_1 \ dt) \otimes (1- i H_2 \ dt)## We can write ## | \phi_i(t) > \ = U_i(t) | \phi_i(0)>## where i can be 1 or 2 depending on the subsystem. The ## U ##'s are unitary time evolution operators. Writing as tensor product we get ## |\phi_1 \phi_2> = (1- i H_1 \ dt) |...
  35. A

    I Which operator for reflection in quantum mechanics?

    Hello, I know we have the parity operator for inversion in quantum mechanics and for rotations we have the exponentials of the angular momentum/spin operators. But what if I want to write the operator that represent a reflection for example just switching y to -y, the matrix in real space...
  36. J

    I How to derive the energy of a parabolic confining potential in a wire

    Hi all, How to derive the energy of a parabolic confining potential in a wire as shown below? I tried to follow the derivation of the harmonic, oscillator like we did for the quantum well and the magnetic field but i can't find anything that has an expression that come close to the one shown...
  37. L

    I Definition of a symmetry transformations in quantum mechanics

    By the Wigner theorem, symmetries transformations are implemented by operators ##\hat{U}## that are unitary or antiunitary. This is what is written in most books. But I have read somewhere that, to ##\hat{U}## represent a symmetrie, it's necessary that ##\hat{U}^{\dagger} \hat{H} \hat{U} =...
  38. JD_PM

    Nucleon-nucleon scattering; why can we assume ##l=0##?

    I have found the following explanation: Isn't ##l \hbar = mvR## (semi-classical argument) wrong? I'd state ##mvR = \sqrt{l(l+1)} \hbar## instead. Text is coming from Introduction to Nuclear Physics; Krane, pages 87 and 88.
  39. P

    I Lawrence Krauss: Quantum Mechanics is deterministic (video)

    I understand partly what he is saying, but can you discount the measurement effect as a feature of the world? Aren't measurement effects going on all the time between macroscopic and microscopic systems, making it in practice, at times, an indeterministic world? Or is he assuming that...
  40. JD_PM

    Calculating the Fraction of Time Particles Spend Outside a Potential Well

    I want to compute the fraction of time both particles spend outside the finite potential well. All I can get is the probability to find them outside. The wavefunction outside the potential is: $$\frac{d^2\psi}{dr^2} = -L^2 \psi$$ Where: $$L = \sqrt{\frac{2mE}{\hbar^2}}$$ Solving the...
  41. A

    Courses Electromagnetism 1 vs. Quantum Mechanics 2

    Hi all, I am an undergraduate junior majoring in materials science who would like some advice with respect to which courses to take for the fall semester of my senior year. Some background: I am a materials science student and I intend to study spintronics and topological insulators for my...
  42. LarryC

    Second Quantization - Quasiparticles

    (Simplified version of Baym, Chapter 19, Problem 2) Calculate, to first order in the inter-particle interaction V(r-r'), the energy of an N+1 particle system of spin-1/2 fermions with on particle of momentum p outside an N-particle Fermi sea (quasiparticle state). The answer should be expressed...
  43. jdou86

    I Confusion about the Concept of Operators

    Dear all, I've been reading and got confused of the concept below have two questions question 1) For <ψ|HA|ψ> = <Hψ|A|ψ>, why does the Hamiltonian operator acting on the bra state and <ψ|AH|ψ> in this configuration it will act on the ket state? question 2) what does it mean for H|ψ> = |Hψ>...
  44. Haorong Wu

    An electron in an oscillating magnetic field

    Homework Statement An electron is at rest in an oscillating magnetic field $$ \mathbf B = B_0 cos\left( ωt \right) \hat k $$ where ##B_0## and ##ω## are constants. What is the minimum field (##B_0##) required to force a complete flip in ##S_x##? Homework Equations $$H=- γ \mathbf B \cdot...
  45. A

    Spin-##\frac{1}{2}## particles in infinite square well

    Homework Statement Construct the four lowest-energy configurations for particles of spin-##\frac{1}{2}## in the infinite square well, and specify their energies and their degeneracies. Suggestion: use the notation ##\psi_{n_1,n_2}(x_1, x_2) |s,m>##. The notation is defined in the textbook...
  46. J

    I Relation between spectral radiance and density of cavity

    Hi, my teacher showed us how we can derive de relation between spectral radiance and density of cavity (of a black hole), but I have a doubt. This is the equation of the energy that are coming from definited directions by the intervals of angles θ and Φ with frequency in a determined interval...
  47. stevendaryl

    I Wallis' Formula and Quantum Mechanics

    Does anybody know what the connection is between Wallis' formula for ##\pi## and quantum mechanics? There was an article about it: https://www.eurekalert.org/pub_releases/2015-11/aiop-ndo110915.php but like all articles for the lay public, all the details were left out. Wallis' formula is...
  48. C

    MATLAB_Quantum Well_Finite Difference Method

    Homework Statement Hi, I am new to MATLAB and have an assignment where I have to construct a Hamiltonian matrix, apply boundary conditions, then find corresponding eigenvalues and eigenvectors for the electron in a box problem. I am stumped where to start. From our class we learned that you...
  49. Peter Morgan

    I Against Collapse: A Mathematical Argument

    One sees "Collapse" language all the time, and yet it seems there's a very simple argument that shows that it's not necessary. Suppose we measure ##\hat A## twice, at an earlier and at a later time, then the joint probability density for the measurement results being ##u## and ##v##...
  50. astrocytosis

    Volume integral over a gradient (quantum mechanics)

    Homework Statement 1) Calculate the density of states for a free particle in a three dimensional box of linear size L. 2) Show that ##\int f \nabla g \, d^3 x=-\int g \nabla f \, d^3 x## provided that ##lim_{r \rightarrow \inf} [f(x)g(x)]=0## 3) Calculate the integral ##\int...
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